There are two electrons inside an infinite potential cube well (essentially $V=\infty$ outside a cube and $0$ inside it) and I need to find the degeneracy of the first excited state. I'm thinking it would be 9 (3 quantum numbers in $x, y, z$ and 3 ways to configure spin to get antisymmetric wavefunction?) but how do I actually get to the right answer?
closed as off-topic by user36790, Jon Custer, honeste_vivere, Floris, Sebastian Riese Oct 16 '16 at 19:18
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Community, Jon Custer, honeste_vivere, Floris, Sebastian Riese
In the first excited state, one of the electrons is excited while the other one is in the ground state. Since the overall wavefunction has to be anti-symmetric it has to be anti-symmetric in the spatial part (since one of the electrons is in the ground state while the other is excited). It furthermore has to be symmetric in the spin part (if it would be anti-symmetric in both the wavefunction and the spin, the total wavefunction would again be symmetric and it would equal zero).